ArticleOpen Access

PARAMETER ESTIMATION OF NONLINEAR OUTPUT ERROR SYSTEM UNDER VARIATIONAL BAYESIAN METHOD BASED ON PROBABILISTIC GRAPHICAL MODEL

Department of Mathematics, Luliang University, Lüliang, Shanxi, P. R. China

Corresponding author.

and

Computer Science Department, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia

E-mail Address: iakatib@kau.edu.sa

Search for more papers by this author

https://doi.org/10.1142/S0218348X22400758Cited by:0 (Source: Crossref)

This article is part of the issue:

Special Issue on Dynamical Systems and Their Applications to Engineering, Economy and Health Sciences
Guest Editors: Juan L. G. Guirao, Elbaz I. Abouelmagd and Bruce A. Wade

Abstract

To estimate the parameters of the nonlinear output error system (nonlinear system), a variational Bayesian estimation method (VB method) is proposed based on the probabilistic graphical model (PGM). First, the related theories are introduced in this study such as the PGM and nonlinear systems. Then, the parameter estimation model of the nonlinear system is established. Finally, a VB method is proposed based on the PGM to estimate the parameters of the nonlinear system, which is tested and verified by numerical simulation experiments. It is found that the parameter estimation model of nonlinear system and the proposed method can estimate the parameters of relevant nonlinear system better, and the minimum error between the parameter estimated value and the actual value is only about 0.0001. It proves the feasibility of the VB method based on PGM in the identification of nonlinear systems. The results of this study provide an important reference for the control and identification of nonlinear systems.

Keywords:

References

1. S. Shin, O. S. Venturelli and V. M. Zavala , Scalable nonlinear programming framework for parameter estimation in dynamic biological system models, PLoS Comput. Biol. 15 (2019) e1006828. Crossref, Web of Science, Google Scholar
2. L. Xu, W. Xiong and A. Alsaedi , Hierarchical parameter estimation for the frequency response based on the dynamical window data, Int. J. Control Autom. Syst. 16 (2018) 1756–1764. Crossref, Web of Science, Google Scholar
3. Y. Wang, F. Ding and M. Wu , Recursive parameter estimation algorithm for multivariate output-error systems, J. Frankl. Inst. 355 (2018) 5163–5181. Crossref, Web of Science, Google Scholar
4. M. A. Z. Raja, A. A. Shah and A. Mehmood , Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system, Neural Comput. Appl. 29 (2018) 1455–1474. Crossref, Web of Science, Google Scholar
5. J. Ding, Z. Cao and J. Chen , Weighted parameter estimation for Hammerstein nonlinear ARX systems, Circuits Syst. Signal Process. 39 (2020) 2178–2192. Crossref, Web of Science, Google Scholar
6. X. Zhang, L. Xu and F. Ding , Combined state and parameter estimation for a bilinear state space system with moving average noise, J. Frankl. Inst. 355 (2018) 3079–3103. Crossref, Web of Science, Google Scholar
7. F. Ding, J. Pan and A. Alsaedi , Gradient-based iterative parameter estimation algorithms for dynamical systems from observation data, Mathematics 7 (2019) 428. Crossref, Web of Science, Google Scholar
8. S. Liu, F. Ding and L. Xu , Hierarchical principle-based iterative parameter estimation algorithm for dual-frequency signals, Circuits Syst. Signal Process. 38 (2019) 3251–3268. Crossref, Web of Science, Google Scholar
9. J. Ding, J. Chen and J. Lin , Particle filtering based parameter estimation for systems with output-error type model structures, J. Frankl. Inst. 356 (2019) 5521–5540. Crossref, Web of Science, Google Scholar
10. L. Xu and F. Ding , Iterative parameter estimation for signal models based on measured data, Circuits Syst. Signal Process. 37 (2018) 3046–3069. Crossref, Web of Science, Google Scholar
11. W. Wöber, G. Novotny and L. Mehnen , Autonomous vehicles vehicle parameter estimation using variational Bayes and kinematics, Appl. Sci. 10 (2020) 6317. Crossref, Google Scholar
12. J. Ma, B. Huang and F. Ding , Parameter estimation of Markov-switching Hammerstein systems using the variational Bayesian approach, IET Control Theory Appl. 13 (2019) 1646–1655. Crossref, Web of Science, Google Scholar
13. S. K. Jain and R. K. Ray , Non-linear diffusion models for despeckling of images: Achievements and future challenges, IETE Tech. Rev. 37 (2020) 66–82. Crossref, Web of Science, Google Scholar
14. M. Babaeian, P. A. Blanche and R. A. Norwood , Nonlinear optical components for all-optical probabilistic graphical model, Nat. Commun. 9 (2018) 2128. Crossref, Web of Science, Google Scholar
15. Q. Ke, S. Wu, M. Wang and Y. Zou , Evaluation of developer efficiency based on improved DEA model, Wirel. Pers. Commun. 102 (2018) 3843–3849. Crossref, Web of Science, Google Scholar
16. A. Arnab, S. Zheng and S. Jayasumana, Conditional random fields meet deep neural networks for semantic segmentation: Combining probabilistic graphical models with deep learning for structured prediction, IEEE Signal Process. Mag. 35 (2018) 37–52. Google Scholar
17. S. Epskamp, L. J. Waldorp and R. Mõttus , The Gaussian graphical model in cross-sectional and time-series data, Multivar. Behav. Res. 53 (2018) 453–480. Crossref, Web of Science, Google Scholar
18. H. Ma, J. Pan and F. Ding , Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems, IET Control Theory Appl. 13 (2019) 3040–3051. Crossref, Web of Science, Google Scholar
19. S. Wu, J. Liu and L. Liu , Modeling method of internet public information data mining based on probabilistic topic model, J. Supercomput. 75 (2019) 5882–5897. Crossref, Web of Science, Google Scholar
20. D. Cabrera, F. Sancho and M. Cerrada , Echo state network and variational autoencoder for efficient one-class learning on dynamical systems, J. Intell. Fuzzy Syst. 34 (2018) 3799–3809. Crossref, Web of Science, Google Scholar
21. X. Zhang, F. Ding and L. Xu , State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle, IET Control Theory Appl. 12 (2018) 1704–1713. Crossref, Web of Science, Google Scholar
22. H. Chen, J. Jiang and D. Cao , Numerical investigation on global dynamics for nonlinear stochastic heat conduction via global random attractors theory, Appl. Math. Nonlinear Sci. 3 (2018) 175–186. Crossref, Google Scholar
23. P. K. Pandey , Solution of two point boundary value problems, a numerical approach: parametric difference method, Appl. Math. Nonlinear Sci. 3 (2018) 649–658. Crossref, Google Scholar
24. M. Dewasurendra and K. Vajravelu , On the method of inverse mapping for solutions of coupled systems of nonlinear differential equations arising in nanofluid flow, heat and mass transfer, Appl. Math. Nonlinear Sci. 3 (2018) 1–14. Crossref, Google Scholar
25. S. Wu, Q. Zhang, W. Chen, J. Liu and L. Liiu , Research on trend prediction of internet user intention understanding and public intelligence mining based on fractional differential method, Chaos Solitons Fractals 128 (2019) 331–338. Crossref, Web of Science, Google Scholar
26. J. Li, F. Deng and J. Chen , A fast distributed variational Bayesian filtering for multisensor LTV system with non-Gaussian noise, IEEE Trans. Cybern. 49 (2018) 2431–2443. Crossref, Web of Science, Google Scholar
27. W. R. Jacobs, T. Baldacchino and T. Dodd , Sparse Bayesian nonlinear system identification using variational inference, IEEE Trans. Autom. Control 63 (2018) 4172–4187. Crossref, Web of Science, Google Scholar
28. J. P. Ruiz-Fernández et al., Influence of seasonal factors in the earned value of construction, Appl. Math. Nonlinear Sci. 4 (2019) 21–34. Crossref, Google Scholar

Vol. 30, No. 02

Metrics

Downloaded 163 times

History

Received 9 January 2021

Accepted 9 July 2021

Published: January 20, 2022

Information

This is an Open Access article in the “Special Issue on Dynamical Systems and Their Applications to Engineering, Economy and Health Sciences”, edited by Juan L.G. Guirao (Technical University of Cartagena, Spain), Elbaz I. Abouelmagd (National Research Institute of Astronomy and Geophysics (NRIAG), Cairo, Egypt) & Bruce A. Wade (University of Louisiana at Lafayette, USA) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Keywords

PDF download

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

PARAMETER ESTIMATION OF NONLINEAR OUTPUT ERROR SYSTEM UNDER VARIATIONAL BAYESIAN METHOD BASED ON PROBABILISTIC GRAPHICAL MODEL

Abstract

Recommended